DE 10 2006 044 952 A1 describes an air duct in a motor vehicle with an inlet opening on the underbody and an outlet opening in the wheel case, through which air is introduced into the wheel case for cooling a brake. The cross section of the outlet opening extends predominantly in the transverse direction of the vehicle. Air that gets into the wheel case via the air duct when driving is for the most part deflected by the tread of the tire and diverted around the brake enveloped by the tire, and thus only contributes little to cooling the brake. In addition, the introduction of air increases the drag inside of the wheel case, which leads to a deterioration in the aerodynamics of the vehicle.